Accuracy and precision are of critical importance in a wide range of ballistics applications, examples of which include target shooting, hunting, self-defense, military, and law enforcement applications. Because the uncertainty associated with the unaided aiming of a firearm or other weapon is often significant, many improvements have been made to increase a shooter's ability to accurately hit an intended target. One such improvement is a telescopic sight, which is also sometimes referred to as a riflescope, or more simply, a scope, which are oftentimes mounted on long guns, but may also be used in conjunction with some handguns. A scope provides improved viewing of the target, for example using optical magnification, and therefore helps the shooter visualize where a projectile will go. In addition to providing magnification, a scope will also often include a reticle having stadia marks or other visual indicia that can be used to facilitate range-finding and to help the shooter adjust for the gravitational and aerodynamic (crosswind) forces that affect the trajectory of a projectile. For example, many reticles provide multiple aiming points for aiming at different distances or under different wind conditions.
Although a properly mounted and calibrated scope will help a shooter compensate for gravitational and aerodynamic forces, the way the firearm is held can still adversely affect the accuracy of the shot. In particular, side-to-side tilt of a scope mounted to a firearm, also referred to as “cant”, is a potentially significant source of inaccuracy, and therefore even if a shooter makes appropriate adjustments for range and windage, his/her shot may still miss its intended target if the scope is canted even slightly off-center. FIGS. 1A and 1B illustrate cant. FIG. 1A illustrates a long gun having an optical system 10, such as a scope, mounted thereon. The optical system 10 has a long axis 12, which may also be referred to as the optical axis or the z axis. FIG. 1B illustrates the view directly along the z axis of the optical system 10, and illustrates two other axes. These axes include a horizontal transverse axis 14, and a vertical transverse axis 16. The transverse axes 14, 16 are both transverse to the z axis. Vertical deflection, or cant, of a system may be measured as deflection of the optical system from the vertical transverse axis 16. For example, an instantaneous axis 18 is not aligned with the vertical transverse axis 16. The mis-alignment between the instantaneous axis 18 and the vertical transverse axis 16 is caused by rotation about the z axis. This rotation amount, also referred to as cant or cant angle, is illustrated in FIG. 1B as the angle θ20.
Canting a firearm to a small or even imperceptible degree can result in significant error downrange, particularly as the distance to the target increases. In a typically mounted scope, the optical axis of the scope is approximately one or two inches above the bore of the firearm. In this case, when the firearm and the scope are canted off-center, the bore of the firearm moves in the opposite direction as the scope. The resulting error manifests as both a horizontal and vertical deflection from the intended target. This error is illustrated in FIG. 2, which is a graph indicating projectile deflection at various ranges as a function of firearm cant angle. The data illustrated in FIG. 2 were modeled based on the trajectory of a 30 caliber, 180 grain Nosler ballistic tip hunting bullet fired from a .300 Winchester Magnum cartridge. At 1500 yards, only 1° of firearm cant results in 20.92 inches (1.74 feet) of horizontal deflection. Canting the firearm 10° results in 12.24 inches (at 500 yards), 65.28 inches (at 1000 yards), or 208.17 inches (at 1500 yards) of horizontal deflection. Vertical deflection is lesser in magnitude than horizontal deflection, but is still significant enough to make an otherwise accurate shot miss its target.
The data illustrated in FIG. 2 demonstrates the importance of reducing or eliminating cant when sighting a target through a scope. In particular, it should be appreciated that even if the shooter's intended target is properly sighted in the scope, a slight—and possibly imperceptible—cant may result in an errant shot. Many shooters rely on an inner sense of balance to ensure that their firearm is not canted. However, this reliance presupposes that the shooter has a fully functional, unimpaired sense of balance that reliably translates into the ability to hold a firearm without any cant. This often turns out not to be the case, particularly for shooters who are exposed to disorienting influences such as loud sounds and strong forces associated with shooting a firearm; repeated focusing on distant targets as viewed through one eye; prolonged periods of standing; exposure to the elements; and traversing or standing upon uneven, canted, and/or sloped terrain.
A number of systems have been developed to supplement a shooter's sense of balance and detect a canted firearm. For example, bubble- and/or fluid-based levels have been adapted for mounting on a firearm, scope, or mounting ring. These systems have limited precision due to fluid viscosity, are subject to freezing in extreme cold, are difficult to see in low light conditions, and often require the shooter to divert his/her attention from the target to determine whether the firearm is canted. For example, mechanical bubble levels are often installed on the exterior body of the riflescope or on an upper portion of a scope ring mount, thus requiring the shooter to move his/her eye away from the sight to see the bubble level. U.S. Pat. No. 6,978,569 discloses various embodiments of a firearm tilt indicator that relies on a physical mechanism, such as a gravity pendulum or a rolling ball. Mechanical systems such as these also often have limited precision, and they tend to fall out of calibration or otherwise fail after repeatedly being subjected to recoil forces. These shortcomings represent substantial obstacles to the development of a robust and reliable cant detection system that does not distract the shooter's attention from the target, and that can be used in a wide range of tactical environments. Other systems that display scope cant are also known, such as gun scope having a full Heads Up Display (HUD), as described in US Patent publication 2014/0184476. Such HUDs act as an opaque screen on which targeting information may be displayed. Other versions may overlay HUD information around the periphery of an optical viewing area. HUDs are generally fragile, expensive, and suffer negatively from exposure to rain, cold and other wet conditions that are often encountered in a typical hunting environment.
Embodiments of the invention address these and other limitations of the prior art.